This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.

In this paper we have studied the optical properties of CuBr thin

films.  Different  sample  thicknesses  have  been  prepared  by  using thermal evaporation  technique with 14.4 runlsec as the average deposition rate and 1 00°C as the substrate temperature.

Polyaniline organic Semiconductor polymer thin films have been prepared by oxidative polymerization at room temperature, this polymer was deposited on glass substrate with thickness 900nm, FTIR spectra was tested , the structural,optical and electrical properties were studied through XRD ,UV-Vis ,IR measurements ,the results was appeared that polymer thin film sensing to NH3 gas.

In the present work, a D.C. magnetron sputtering system was
designed and fabricated. This chamber of this system includes two
coaxial cylinders made from copper .the inner one used as a cathode
while the outer one used as a node. The magnetic coils located on
the outer cylinder (anode) .The profile of magnetic field for various
coil current (from 2Amp to 14Amp) are shown. The effect of
different magnetic field on the Cu thin films thickness at constant
pressure of 7x10-5mbar is investigated. The result shown that, the
electrical behavior of the discharge strongly depends on the values
of the magnetic field and shows an optimum value at which the
power absorbed by the plasma is maximum. Furthermore, the
pl

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to simulate values of the variable coefficients as random sampling instead being limited as real values with respect to time. The mean of the n final solutions via this integrated technique, named in short as mean Monte Carlo finite difference (MMCFD) method, represents the final solution of the system. This method is proposed for the first time to calculate the numerical solution obtained fo

Laue back reflection patterns for quartz crystal are indexed by using Orient Express- program to simulate orientation of single crystals from assignment of principle zones. An oriented quartz single crystal was used as a substrate to deposit Zn metal by controlled thermal evaporation to achieve single crystal films of Zn that are subsequently evaluated by x-ray powder diffraction.

This paper sheds the light on the vital role that fractional ordinary differential equations(FrODEs) play in the mathematical modeling and in real life, particularly in the physical conditions. Furthermore, if the problem is handled directly by using numerical method, it is a far more powerful and efficient numerical method in terms of computational time, number of function evaluations, and precision. In this paper, we concentrate on the derivation of the direct numerical methods for solving fifth-order FrODEs  in one, two, and three stages. Additionally, it is important to note that the RKM-numerical methods with two- and three-stages for solving fifth-order ODEs are convenient, for solving class's fifth-order FrODEs. Numerical exa

In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.